## anonymous 5 years ago let f(x) = lxl is f continuous at x = 0 why ????????

1. dumbcow

f is continuous because there are no gaps in the graph, in other words the point x=0 is defined -> f(0) = |0| = 0

2. anonymous

this is exact question i wrote ,,,, i also dont know ,,,,,

3. dumbcow

For a counter example imagine f(x) =|x| for x<0 and x>0 but f(x) = 1 for x=0 This means the y value jumps up 1 when you go from .00001 to 0 there is a gap

4. dumbcow

make sense??

5. anonymous

yes ,,,

6. anonymous

thnx

7. anonymous

8. anonymous

yes

9. anonymous

The function is continuous if $$\lim_{x \rightarrow c^+} f(x) = \lim_{x \rightarrow c^-} f(x) = f(c)$$

10. anonymous

i am new with limits ,,,

11. anonymous

As x gets closer and closer to c either from the -infinity or +infinity sides, the function must approach the value f(c) in order to be continuous For f(x) = |x| we see that the limit from the left is approaching f(0)=0 along the y=-x line. From the right we see it's approaching f(0) = 0 along the y=x line. Also the value of the function at x = 0 is 0 which is the value being approached from the left and the right. Therefore it is continuous about 0. (in fact it is continuous everywhere).

12. anonymous

k ,,,, thnx a lot ,,,,,,,,,